Optimal. Leaf size=44 \[ \frac {2401}{176 (1-2 x)}+\frac {621 x}{50}+\frac {81 x^2}{40}+\frac {33271 \log (1-2 x)}{1936}+\frac {\log (3+5 x)}{15125} \]
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Rubi [A]
time = 0.01, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {81 x^2}{40}+\frac {621 x}{50}+\frac {2401}{176 (1-2 x)}+\frac {33271 \log (1-2 x)}{1936}+\frac {\log (5 x+3)}{15125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac {621}{50}+\frac {81 x}{20}+\frac {2401}{88 (-1+2 x)^2}+\frac {33271}{968 (-1+2 x)}+\frac {1}{3025 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{176 (1-2 x)}+\frac {621 x}{50}+\frac {81 x^2}{40}+\frac {33271 \log (1-2 x)}{1936}+\frac {\log (3+5 x)}{15125}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 45, normalized size = 1.02 \begin {gather*} \frac {6723}{1000}+\frac {2401}{176-352 x}+\frac {621 x}{50}+\frac {81 x^2}{40}+\frac {33271 \log (5-10 x)}{1936}+\frac {\log (3+5 x)}{15125} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 35, normalized size = 0.80
method | result | size |
risch | \(\frac {81 x^{2}}{40}+\frac {621 x}{50}-\frac {2401}{352 \left (-\frac {1}{2}+x \right )}+\frac {33271 \ln \left (-1+2 x \right )}{1936}+\frac {\ln \left (3+5 x \right )}{15125}\) | \(33\) |
default | \(\frac {81 x^{2}}{40}+\frac {621 x}{50}-\frac {2401}{176 \left (-1+2 x \right )}+\frac {33271 \ln \left (-1+2 x \right )}{1936}+\frac {\ln \left (3+5 x \right )}{15125}\) | \(35\) |
norman | \(\frac {-\frac {87349}{2200} x +\frac {4563}{200} x^{2}+\frac {81}{20} x^{3}}{-1+2 x}+\frac {33271 \ln \left (-1+2 x \right )}{1936}+\frac {\ln \left (3+5 x \right )}{15125}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 34, normalized size = 0.77 \begin {gather*} \frac {81}{40} \, x^{2} + \frac {621}{50} \, x - \frac {2401}{176 \, {\left (2 \, x - 1\right )}} + \frac {1}{15125} \, \log \left (5 \, x + 3\right ) + \frac {33271}{1936} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 50, normalized size = 1.14 \begin {gather*} \frac {980100 \, x^{3} + 5521230 \, x^{2} + 16 \, {\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 4158875 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 3005640 \, x - 3301375}{242000 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 36, normalized size = 0.82 \begin {gather*} \frac {81 x^{2}}{40} + \frac {621 x}{50} + \frac {33271 \log {\left (x - \frac {1}{2} \right )}}{1936} + \frac {\log {\left (x + \frac {3}{5} \right )}}{15125} - \frac {2401}{352 x - 176} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.63, size = 63, normalized size = 1.43 \begin {gather*} \frac {27}{800} \, {\left (2 \, x - 1\right )}^{2} {\left (\frac {214}{2 \, x - 1} + 15\right )} - \frac {2401}{176 \, {\left (2 \, x - 1\right )}} - \frac {34371}{2000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {1}{15125} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 30, normalized size = 0.68 \begin {gather*} \frac {621\,x}{50}+\frac {33271\,\ln \left (x-\frac {1}{2}\right )}{1936}+\frac {\ln \left (x+\frac {3}{5}\right )}{15125}-\frac {2401}{352\,\left (x-\frac {1}{2}\right )}+\frac {81\,x^2}{40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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